Raskind–Spiess conjecture on the Albanese kernel of varieties over p-adic fields

Let $k$ be a finite extension of $\mathbb{Q}_p$ and let $Y$ be a smooth projective geometrically connected variety over $k$. Write $T(Y)$ for the kernel of the Albanese map on the degree-zero Chow group of $Y$.

Raskind–Spiess conjecture. The group $T(Y)$ is the direct sum of its maximal divisible subgroup and a finite group.

This conjecture concerns the non-divisible part of the Albanese kernel over a $p$-adic field and is motivated by work of Colliot-Thélène. Its resolution is not specified in the source.